Advertisements
Advertisements
Question
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
Advertisements
Solution
Conjunction of two statement p and q is symbolically written as p ∧ q.
RELATED QUESTIONS
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
[~(~p ∧ ~q)] v q
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
Write the following statement in symbolic form.
It is not true that “i” is a real number.
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
If p and q are true and r and s are false, find the truth value of the following compound statement.
p ∧ (q ∧ r)
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
Proof is lengthy and it is not interesting.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is interesting iff the proof is lengthy.
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
(p ∧ q) ∨ r
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
Find the negation of 10 + 20 = 30
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.
Which of the following is false?
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
Let S be a non-empty subset of R. Consider the following statement:
p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
From the following set of statements, select two statements which have similar meaning.
- If a man is judge, then he is honest.
- If a man is not a judge, then he is not honest.
- If a man is honest, then he is a judge.
- If a man is not honest, then he is not a judge.
Write the negation of p ↔ q.
